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Nonlinear Dynamics

, Volume 66, Issue 1–2, pp 133–139 | Cite as

Numerical approximation of a class of discontinuous systems of fractional order

  • Marius-F. DancaEmail author
Original Paper

Abstract

In this paper we investigate the possibility to formulate an implicit multistep numerical method for fractional differential equations, as a discrete dynamical system to model a class of discontinuous dynamical systems of fractional order. For this purpose, the problem is continuously transformed into a set-valued problem, to which the approximate selection theorem for a class of differential inclusions applies. Next, following the way presented in the book of Stewart and Humphries (Dynamical Systems and Numerical Analysis, Cambridge University Press, Cambridge, 1996) for the case of continuous differential equations, we prove that a variant of Adams–Bashforth–Moulton method for fractional differential equations can be considered as defining a discrete dynamical system, approximating the underlying discontinuous fractional system. For this purpose, the existence and uniqueness of solutions are investigated. One example is presented.

Keywords

Fractional systems Discontinuous systems Chaotic attractors Filippov regularization Adams–Bashforth–Moulton method for fractional differential equations 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Dept. of Mathematics and Computer ScienceAvram Iancu UniversityCluj-NapocaRomania
  2. 2.Romanian Institute of Science and TechnologyCluj-NapocaRomania

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